A drilling device for surgical proposes is described in EPO application EP-A 90109556.2. It consists essentially of drive means, for example a compressed air turbine or an electrical motor, an angle attachment that can be connected with the drive means via a coupling, and a drill bit connected to the angular attachment. The angular attachment is made of a material that, at least as regards its components adjacent the drill bit, is X-ray permeable. This gives the surgeon unhindered image converter control, so that the operating field is visible to him on an X-ray screen without dark areas of any kind being created by the drilling device. This makes this device suitable for various osteosynthetic procedures, including the positioning of locking holes during intramedullary nailing. Particularly in intramedullary nailing, because of the anatomical-geometrical conditions, angle gear attachments of this type are used. The drill bit in this case can be connected, permanently or via a suitable coupling, with the drive shaft of the angle attachment. However, during an operation, it may be necessary to change one drill bit for another, for example one with a large diameter, as quickly as possible. Drilling devices according to this prior design are not well adapted to this.